Previews-Amca 200 R2011 Pre

AMCA Publication 200-95 (R2011)  Air Systems

AIR  MOVEMENT AND  CONTROL ASSOCIATION INTERNATIONAL,   INC. The International Authority on Air System Components

AMCA PUBLICATION 200-95 (R2011)

Air Systems

Air Movement and Control Association International, Inc. 30 West University Drive Arlington Heights, IL 60004-1893

© 2011 by Air Movement and Control Association International, Inc.  All rights reserved. Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the United States Copyright Act without the permission of the copyright owner is unlawful. Requests for  permission or further information should be addressed to the Executive Director, Air Movement and Control  Association International, Inc. at 30 West University Drive, Arlington Heights, IL 60004-1893 U.S.A.

Authority  AMCA Publication 200-95 was adopted by the membership of the Air Movement and Control Association International, Inc. in 1995, and it was reaffirmed in 2000, 2007, and 2011.

Foreword This publication is intended to provide basic information needed to design effective and energy efficient air  systems. in those cases where the system handles a gas other than air, the design data must be modified to allow for the different physical properties of the gas being used. Discussion is limited to systems where there is a clear separation of the fan inlet and outlet and does not cover  applications in which fans are used only to circulate air in an open space. The design of most air sytems is based on airflow velocities which result in turbulent airflow. Some applications require very low velocities, resulting in laminar flow conditions; others may require very high velocities, approaching the speed of sound (Mach 1). The information given in this publication applies only to turbulent flow conditions and not to these special systems using very low or very high flow velocities. The flow through an air system will stabilize when the total pressure provided by the fan is exactly equal to the total pressure losses in the system. To achieve the desired airflow in the system the diesgner must have complete information on: a)

System Pressure Losses: The total pressure loss due to friction losses, shock losses, dissipation of velocity pressure at the system discharge, and static pressure differences between the entry and discharge openings. System pressure losses are discussed in detail in Section 4.

b)

Fan Performance Characteristics: The relationship of the total pressure rise and the volume flow generated by the fan. Fan performance characteristics are reviewd in Section 5. More complete information is contained in AMCA Publication 201, Fans and Systems.

c)

System Effect: The effect on the performance of the fan resulting from the difference between the fan inlet and outlet connections to the installed system and the standardized connections used in laboratory tests to obtain fan performance ratings. A practical approach to estimating System Effects is explained in AMCA Publication 201, Fans and Systems.

AMCA 200 Review Committee Robert H. Zaleski, Chairman

Acme Engineering & Manufacturing Corp.

Jack E. Saunders

Barry Blower/McQuay International

Neil H. Rutherford

Delhi Industries, Inc.

Charles R. Voss

Phelps Fan Manufacturing Co., Inc.

Robert L. Lanier

Phelps Fan Manufacturing Co., Inc.

William Smiley

The Trane Company

Paul R. Saxon

AMCA Staff  

Disclaimer  This manual has been prepared by the Air Movement and Control Association, Inc. The information contained in this manual has been derived from many sources and is believed to e accurate. Please note that the recommendations contained herein do not necessarily represent the only methods or procedures appropriate for  the situation discussed, but rather are inteded to present consensus opinions and practices of the air movement and control industry which may be helpful, or of interest to those who design, test, install, operate or maintain fanduct systems. Thus, AMCA disclaimes any and all warranties, expressed or implied, regarding the accuracy of the information contained in this maual and further disclaims any liability for the use or misuse of this information.  AMCA does not guarantee, certify or assure the performance of any fan-duct system designed, tested, installed, operated or maintained on the basis of the information provided in this manual.

Objections to AMCA Standards and Certifications Programs  Air Movement and Control Association International, Inc. will consider and decide all written complaints regarding its standards, certification programs, or interpretations thereof. For information on procedures for submitting and handling complaints, write to:  Air Movement and Control Association International 30 West University Drive  Arlington Heights, IL 60004-1893 U.S.A. or   AMCA International, Incorporated c/o Federation of Environmental Trade Associations 2 Waltham Court, Milley Lane, Hare Hatch Reading, Berkshire RG10 9TH United Kingdom

Related AMCA Standards and Publications

Publication 200

AIR SYSTEMS 

System Pressure Losses Fan Performance Characteristics System Effect System Design Tolerances  Air Systems is intended to provide basic information needed to design effective and energy efficient air systems. Discussion is limited to systems where there is a clear separation of the fan inlet and outlet and does not cover  applications in which fans are used only to circulate air in an open space. Publication 201

FANS AND SYSTEMS 

Fan Testing and Rating The Fan "Laws"  Air Systems Fan and System Interaction System Effect Factors Fans and Systems is aimed primarily at the designer of the air moving system and discusses the effect on inlet and outlet connections of the fan's performance. System Effect Factors, which must be included in the basic design calculations, are listed for various configurations. AMCA 202 and AMCA 203 are companion documents. Publication 202

 

TROUBLESHOOTING 

System Checklist Fan Manufacturer's Analysis Master Troubleshooting Appendices Troubleshooting  is intended to help identify and correct problems with the performance and operation of the air  moving system after installation. AMCA 201 and AMCA 203 are companion documents. Publication 203

FIELD PERFORMANCE MEASUREMENTS OF FAN SYSTEMS 

 Acceptance Tests Test Methods and Instruments Precautions Limitations and Expected Accuracies Calculations Field Performance Measurements of Fan Systems  reviews the various problems of making field measurements and calculating the actual performance of the fan and system. AMCA 201 and AMCA 202 are companion documents.

TABLE OF CONTENTS

1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Air system components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.

Symbols and Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Symbols and subscripted symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.

Properties of Air   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1 Properties of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.

Airflow

...................................................................... 5

4.1 Flow conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.2 Flow about immersed bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.3 Ducted flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.4 System losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.5   System Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.

The Flow System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.1 Concepts of pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.2 Examples of pressures in duct systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.3 Conservation of energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.4 Fan total and static pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.5 The total system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.6 Types of fan system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.7 System resistance factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.8 System design and loss calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.9 Density effects in air systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.

System Design and Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.1 Point of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.2 Fan performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6.3 Effects of system changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.4 Variable systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Annex A.

SI / I-P Conversion Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Annex B.

Standard Atmospheric Data Versus Altitude Charts . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Annex C.

Psychrometric Density Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Annex D.

Friction Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Annex E.

Air Density Correction Factor Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

 AMCA INTERNATIONAL, INC.

Air Systems 1. Introduction  An air system is any assembly of ducts, filters, conditioning devices, dampers, louvers, fans, etc., the main purpose of which is to move air from one place to another in a controlled fashion. Most air  systems draw air from one space and discharge it into another.  Air syste ms are often required to operate satisfactorily in a wide range of environmental conditions. The conditions which will be encountered must be considered in the design of the ducts, pipes, etc., which will contain the airflow and constitute the boundary of the system.

1.1 Air system components  A typical air system may contain one or more of the following (see Figure 1): a) b) c) d) e) f)

System inlet Distribution system Fan Control device Conditioning device System outlet

1.1.1 System inlet. An air system usually includes devices such as louvers, filters, screens, guards, grilles, etc., where the air enters the system. These are used for safety reasons as well as to inhibit the entry of rain, dust, and other unwanted matter. Their  appearance may be important as they are usually visible on the exterior of a structure. 1.1.2 Distribution system. Most air systems are made up of ducts specially designed and constructed to convey air from the system inlet(s) to the system outlet(s). In some cases, enclosed spaces in the structure such as plenums above ceilings or holes in walls may be used to confine and direct the flow. 1.1.3 Fan. Understanding the design and opera-tion of air systems begins with an understanding of the

AMCA 200-95 (R2011) various types of fans, their performance characteristics, and their applications.  A fan is required in order to produce the pressure differential which results in the flow of air through a system. The fan must be carefully selected to meet the specified airflow and pressure for proper system operation. Different fan designs produce different pressure-volume and fan power relationships, which are critical to air system operation. Refer to Figure 4.2, AMCA Publication 201-90. 1.1.4 Control devices.   In many air systems it is necessary to regulate and control the flow through the system in response to some monitoring signal, usually temperature or pressure. It may be also necessary to regulate the flow in the individual branches of the system. Control devices such as dampers function by controlling the amount of airflow. In some cases, the output of the fan can be varied by other methods (variable speed motor, variable inlet vanes, variable pitch impeller, etc.) 1.1.5 Conditioning device. Most air systems are designed to take air from the inlet and change its condition before discharging it at the outlet. Changes may include the temperature, humidity, pressure, contaminant level and cleanliness, etc., of the air. Many conditioning devices require outside energy sources, for example, heating and cooling coils; other  components such as filters are passive devices and have no external energy connection. All conditioning devices increase the pressure drop across the system and this effect must be considered in the selection of the fan. 1.1.6 System outlet. An air system usually includes a special component at the termination of the system or at the end of each of the system's branches, such as a simple screen or louver. In many cases the distribution of the air at the outlet to the receiving space is very important, e.g., in an occupied air  conditioned room. These systems require carefully selected outlets and diffusing devices to achieve desirable air motion and temperature conditions in the conditioned space. Typical devices are ceiling diffusers and grilles. In some cases these may incorporate control devices such as dampers and mixing boxes.

1

 AMCA 200-95 (R2011)

FAN

MAIN DISTRIBUTION SYSTEM (DUCT)

SYSTEM INLET

BRANCH DUCT

COIL FILTER LOUVER

DAMPER DIFFUSER SYSTEM OUTLET

Figure 1 - Typical Air System

2

SYSTEM OUTLET

SYSTE OUTLE

 AMCA 200-95 (R2011)

2. Symbols and Subscripts 2.1 Symbols and subscripted symbols Symbol

Description

SI

 A  Ae  Ao ah C  C d C n c  D E  ε  f  g 

Area Area-Orifice Equivalent to System Area-Nozzle with no loss Absolute Humidity Dynamic Loss Coefficient Coefficient of Discharge Coefficient of Nozzle Discharge Speed of Sound Duct Diameter and Equivalent Diameter System Resistance Curve Absolute Surface Roughness Height Friction Coefficient Gravity Ratio of Specific Heats System Effect Factor (System) Length Air Viscosity, Absolute Pressure Differential Pressure Static Pressure Static Pressure at Plane x Total Pressure Total Pressure at Plane x Velocity Pressure Atmospheric Pressure Airflow Rate Airflow Rate at Plane x Gas Constant Reynolds Number Relative Humidity Air Density Air Density at Plane x System Effect Factor (Fan) System Resistance Factor Specific Humidity (_/_ dry air) Temperature Dry-Bulb Temperature Wet-Bulb Temperature Average Velocity Velocity - At any Point Expansion Factor Altitude Is Proportional to

m2 (ft2) 2 m (ft2) m2 (ft2) kg/m3 (lb/ft 3) Dimensionless Dimensionless Dimensionless m/s (ft/s) m (ft) Dimensionless m (ft) Dimensionless m/s2 (ft/s2) Dimensionless Dimensionless m (ft) N-s/m2 (lbm/ft-s) Pa (in. wg) Pa (in. wg) Pa (in. wg) Pa (in. wg) Pa (in. wg) Pa (in. wg) Pa (in. wg) Pa (in. Hg) m3/s (cfm) m3/s (cfm) J/kg-K (ft-lb/lbm-°R) Dimensionless % (%) 3 kg/m (lbm/ft 3) kg/m3 (lbm/ft 3) Pa (in. wg) -4 m (ft-4) kg/kg dry air (lb/lb) dry air   °C (°F) °C (°F) °C (°F) m/s (ft/min) m/s (ft/min) Dimensionless m (ft) Dimensionless

γ 

K  L  µ

 ∆P  P  P s P sx P t P tx P v  p Q Qx R  Re rh

   

 ρ  ρx

SEF  S R sh t  t d t w V  v  Y  Z  ~

(I-P)

2.2 Subscripts Subscript

Definition

Subscript

Definition

a b c d E F

Element a Element b Element c - Combined Discharge Plane of System Entry Fan

n O x x,x' 1 2

Reference to Nozzle Plane of System Outlet Plane 0, 1, 2,...as appropriate Between Planes x and x' Plane of Fan Inlet Plane of Fan Discharge 3

 AMCA 200-95 (R2011)

3. Properties of Air   Atmospheric air is a mixture of several gases, water  vapor, and impurities. The relative amounts of the important constituents for dry, sea level air are given in Table 3.1. This table may be considered representative of air at any altitude. Table 3.1 - Dry Air Composition, Fraction Component

Volume

Weight

Nitrogen

0.7809

0.7552

Oxygen

0.2095

0.2315

 Argon

0.0093

0.0128

Carbon Dioxide

0.0003

0.0004

 Also slight traces of neon, hydrogen, helium, krypton, ozone and others  Although the gas composition of air can be considered essentially constant, the amount of water  vapor contained in the air can vary greatly. The properties of moist air are dependent upon the relative amount of water vapor and dry air, therefore, in defining the properties of moist air, this relative amount must be defined (see Section 3.1.5 Humidity). The impurities in the air are of various forms, but basically can be divided into two categories: a) particulates which can be either solid or liquid, and b) mixtures, which can be either gas or vapor. The distribution of these impurities is not uniform on an atmospheric scale, but can be considered uniform for  the purposes of air system design. Since air is a mixture of several gases, the behavior of air under  varying conditions can be best understood by first reviewing the behavior of pure gases.

3.1 Properties of gases  A gas may be defined as a compressible substance which has no free surfaces and occupies all portions of its container. The important properties of an ideal gas are listed below. 3.1.1 Density. The density of a gas is defined as the total mass of the molecules in a unit volume. In the SI system density is given in kilograms per cubic meter (kg/m3); in the I-P system, density is given in pounds per cubic foot (lbm/ft3). For purposes of uniformity, standard air has been defined as air with a density of 1.2 kg/m3 (0.075 lbm/ft 3) and an absolute viscosity of 18.19 × 10-6 4

N-s/m2 (1.222 × 10-5 lbm/ft-s). This is substantially equivalent to air at a temperature of 20°C (68°F), 50% relative humidity, and a barometric pressure of  101 kPa (29.92 inches mercury) at sea level. The ratio of specific heats, ( γ ), is taken to be 1.4, which is the expected value for a perfect diatomic gas. The temperature and barometric pressure of  atmospheric air vary widely with weather conditions and geographical location, most noticeably altitude. In order to simplify design, standard atmospheric conditions have been defined which give the variation of atmospheric pressure, temperature, and, therefore, density with altitude. Annex B lists these variations. 3.1.2 Pressure. In an air system, pressure is the force exerted by the air molecules on the surfaces which make up the system. Since air molecules are always in motion, they continuously collide with other  air molecules or a solid surface. All these collisions are considered to be perfectly elastic and, in the case when a molecule strikes a surface, the surface experiences a force equal and opposite to the time rate of change of momentum of the rebounding molecule. This force causes the gas to exert an overall pressure on an immersed body and this force per unit area is referred to as the pressure. In air  system work, the units of pressure are given in terms of force per unit area. The unit of measure for  pressure in the SI system is the Pascal (Pa); in the I-P system the units are inches of water gauge (in. wg). 3.1.3 Temperature 3.1.3.1 Thermal relationships. The kinetic energy of gas molecules increases with increasing temperature. The important effects of this fact are stated in Boyle's Law and Charles' Law, which state that the volume of a perfect gas varies inversely with absolute pressure and directly with absolute temperature, respectively. The total effect is more properly stated by the equation of state: PV  =  mRT 

Eq. 3.1-1

or  P  = ρRT  Where: P   = Pressure V   = Volume m   = mass R = Gas Constant T  = Absolute Temperature  ρ = m/V   = density

Eq. 3.1-2

 AMCA 200-95 (R2011) In the design of most air systems, it is acceptable to assume that the gas is incompressible, therefore, the air density may be considered constant, and therefore, the absolute pressure and absolute temperature are directly proportional. 3.1.3.2 Dry-bulb, wet-bulb and dew point temperature. Unless otherwise specified, the temperature of an air-water vapor mixture is that temperature which is indicated by an ordinary or drybulb thermometer. This dry-bulb temperature is the temperature of both the air and the water vapor in the mixture. The wet-bulb temperature may be determined by exposing a wetted bulb in a moving air-water vapor mixture until equilibrium is obtained. The wet-bulb temperature will be lower than the drybulb temperature as long as evaporation continues. If no evaporation is possible, the mixture is saturated and the wet and dry-bulb temperatures for this condition will be identical. The dew point temperature of an air-water vapor mixture is the saturation temperature corresponding to the absolute humidity of the mixture. The dew point temperature may also be considered as that temperature at which condensation begins when the mixture is gradually cooled. 3.1.4 Viscosity. A non-perfect gas, such as air, is capable of exerting a force parallel to the surface of a body which is moving with respect to the gas. The magnitude of the force parallel to the surface is used to define an important property of non-perfect gases - viscosity. The effects of viscosity on the behavior of  real gases cause resistance to flow; the resistance is proportional to the velocity gradients which exist in the gas. The absolute viscosity (�) is defined as the shearing stress for a unit rate of change of velocity. The absolute viscosity has units of newton-sec per  meter squared (N-s/m2) in the SI system and pound mass per foot-second (lbm/ft-s) using I-P units. 3.1.5 Humidity. The density of atmospheric air is also a function of the humidity. Although the change in density due to a change in humidity is not large, it is often significant and air system designers should be aware of these changes. Remember that increasing humidity lowers the density since water  vapor is lighter than dry air. The density of saturated air for various barometric and hygrometric conditions is shown in Annex C. Partially saturated air contains vapor that is superheated, that is, the temperature of the mixture and, therefore, that of the vapor is higher than the saturation temperature for the existing vapor  pressure. The relative humidity (rh) of an air-water vapor 

mixture is defined as the ratio of the vapor pressure existing compared to the vapor pressure at saturation for the same dry-bulb temperature. This is also equal to the ratio of the mole fractions under the same condition. Relative humidity is always expressed as a percent. Specific humidity (sh) is the actual mass (weight) of  the water vapor existing per unit mass (unit weight) of  dry air or gas. Absolute humidity (ah) may be expressed in kilograms (pounds) of water vapor per  cubic meter (cubic foot) of mixture. The humidity of  an air-water vapor mixture is often expressed by giving either relative humidity or a wet-bulb depression.

4. Airflow The flow of any fluid between two points is caused by the existence of a pressure differential between the two points. It is the purpose of this section to explain the parameters that may affect the flow of a gas between two points.

4.1 Flow conditions Most air systems are designed in the incompressible range. Where compressibility is a factor, Mach number and Reynolds number must be considered. The magnitude of these parameters gives an indication of the effects which can be expected from the deviations in the non-perfect gas behavior from that of a perfect gas. 4.1.1 Mach number . Mach number, for our purposes here, is the ratio of the velocity of an airstream to the speed of sound in that airstream. Mach number = V /c  Where: V  = velocity of air, m/s (ft/s) c  = speed of sound in air, m/s (ft/s) The speed of sound is a function of temperature and is the speed at which very small pressure disturbances are propagated throughout the gas. The speed of sound is proportional to the square root of the absolute temperature, and for standard air is approximately 345 m/s (1130 ft/s). If the Mach number is small and no large static pressure changes are introduced by mechanical means, the flow may be considered incompressible, that is, the density is everywhere constant. Air can be considered incompressible if the fan total pressure rise is less than 2980 Pa (12 in. wg). 5

 AMCA 200-95 (R2011) 4.1.2 Reynolds number . The ratio of the inertia force to the viscous force caused by changes in velocity within the fluid element is known as the Reynolds number.

Re

     = DV         

     = DV       60  

Re

Eq. 4.1-1A SI

Eq. 4.1-1A I-P

when in contact with the body. This is called skin friction drag, and, for streamlined bodies closely aligned with the flow, represents the entire drag force. For blunt bodies, which may be streamlined bodies at large angles to the flow, profile drag exists. Profile drag is caused by the inability of the flow, due to its viscous effects, to follow the body shape. The inability to follow the body shape creates a wake of  very turbulent flow which in effect creates the profile drag force. These wake effects are the predominant cause of flow losses in systems.

  DV    =         For standard air: Re = 65970.3DV  Re = 102.3DV 

Eq. 4.1-1B SI Eq. 4.1-1B I-P

Figure 4A - Skin Friction Drag

Where: D = Any convenient reference dimension, m (ft) V  = Velocity, m/s (ft/min)  µ = Absolute viscosity, N-s/m2 (lbm/ft-s) γ  = Kinematic viscosity, m2/s (ft2/s)  ρ = Density, kg/m3 (lbm/ft 3) For flow about immersed bodies, D  is normally taken as the length of body in the direction of flow. In ducted flow, D   is normally taken as the diameter of  the duct; in unducted flow, D is normally taken as the diameter of the opening through which the flow passes. For a fan, D  is equal to the impeller tip diameter and is only proportional to conventional Reynolds numbers. The Reynolds number provides a convenient non-dimensional means of comparing two flows.

4.2 Flow about immersed bodies If a solid body is immersed in a flowing stream of a gas, the direction of flow of the gas will be parallel to the surface of the solid body. The changes in the direction of the molecules close to the body exert forces on the body which when taken over the entire body, are perpendicular to the direction of the gas flow.  A non-perfect gas will also exert a force parallel to the direction of the velocity, due to the viscosity of the gas. This force, usually called drag, is due to two effects. The first is the shearing force set up within the molecules of the gas resulting from the molecules decelerating from the gas velocity to zero velocity 6

Figure 4B - Profile Drag Figures 4A and 4B illustrate skin friction drag and profile drag.

4.3 Ducted flow When air flows through a duct of constant crosssection, the average velocity remains constant and is parallel to the center line of the duct. Due to friction, the velocity at the duct wall is zero and the average velocity profile can be defined as either of two conditions: a) Laminar Flow: Flow in which the air velocity vectors are parallel to the duct wall. This type of  flow is described as smooth. b) Turbulent Flow: Flow in which air velocity vectors at various points across the duct are at various angles, up to and including reverse flow. Except for extremely low air velocities, laminar flow does not exist and all duct flow involving air can be considered to be in the transition region between laminar and fully turbulent flow. The transfer of 

 AMCA 200-95 (R2011) energy from the high velocity section in the center of  the duct to the low velocity section near the duct wall causes a marked resistance to the flow. This resistance varies linearly with the length of the duct and approximately with the square of the average velocity in the duct. The resistance is also a function of the Reynolds number of the flow, which is calculated using the average velocity in the duct, the duct diameter, and the surface roughness of the duct wall. The velocity profiles in a duct system for fully developed flow will vary depending on whether the flow is laminar or turbulent and the degree of duct roughness. Velocity profiles of various flow conditions are shown in Figure 4C. The absolute velocity of the air stream will vary substantially over the cross-sectional duct area, but for duct systems the velocity used for determining the velocity pressure is always the average velocity given by: V  average = Q/ A

Eq. 4.3-1

In addition to the losses in total pressure in a system caused by friction losses and dynamic losses, there are losses due to System Effects. System Effects   occur because of the differences between the fan inlet and outlet connections to the installed system and the standardized connections used in laboratory tests to obtain fan performance ratings. AMCA Publication 201,  Fans and Systems, gives specific details on   System Effects   related to fans.   System Effects   related to series system elements are covered further in Section 4.5 of this publication. 4.4.1 Duct friction losses. In the normal range of air  systems for HVAC and industrial applications, the flow falls into the transition region between laminar  flow and complete turbulent flow. In this region the losses due to friction are a function of Reynolds number and the relative roughness of the duct wall. The pressure loss in the transition region will vary at slightly less than the square of the velocity. The pressure loss due to friction for flow in ducts may be calculated from the Darcy-Weisbach equation:

Where:

 ∆P t  =  f (L/D) P v

V  = Velocity, m/s (ft/min) Q = Flow rate, m3/s (cfm)  A  = Area of the cross-section where the flow occurs, m2 (ft2)

Where:

The duct velocity profiles shown in Figure 4C are uniform along the length of the duct and symmetrical around the center line. Where there are disturbances in the ducts, such as turns, expansion or contraction, etc., the velocity profile across the duct can become very asymmetrical as shown in Figure 4D. The flow will return to a normal velocity profile after a disturbance if there is sufficient length of straight duct to allow the velocity distribution to regain uniformity.  A minimum of 2½ equivalent duct diameters of  straight duct is required to attain a normal velocity profile for velocities of 12.7 m/s (2500 ft/min) or less.  Add one duct diameter for each additional 5.08 m/s (1000 ft/min). See AMCA Publication 201-90, Fans and Systems.

4.4 System losses The losses in total pressure for flow through a system are caused by two factors:   friction losses   due to viscosity as the air flows along the surface of ducts and other system elements, and  dynamic losses due to the turbulent wake caused by changes in direction and separation of the flow around obstructions.

 ∆P t  = f  = L = D = P v =

Eq. 4.4-1

Total pressure loss due to friction, Pa (in. wg) Friction factor, dimensionless Length of duct, m (ft) Diameter of pipe, m (ft) Velocity pressure, Pa (in. wg)

In the transition flow range, the value of the friction factor cannot be calculated directly. It can be obtained from the Moody diagram or by iterative solution of the Colebrook equation. See the  ASHRAE Handbook: Fundamentals, chapter on Duct  Design, for a more complete discussion of duct friction losses. The Moody diagram, Figure 4E, shows the relationship of the friction factor, Reynolds number  and duct roughness (ε ) in meters (feet). Most applications are in the transition region between laminar and full turbulent flow conditions. Using duct friction charts (see Annex D) is the most common method of determining friction losses. These charts are based on ducts having average roughness and standard air density. Correction factors must be applied for ducts having different roughness, and for variations in air density and viscosity.

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 AMCA 200-95 (R2011)

LAMINAR

r 

TURBULENT

SMOOTH Re = 10 7 SMOOTH Re = 105 ε  = 0.03D ROUGH ε  = 0.008D ROUGH

0

0.5

1.0

1.5

v  V  D

= Duct Diameter  ε  = Duct Roughness Re = Reynolds Number  v  = Velocity at any Point V  = Average Velocity r  = Radius Figure 4C - Velocity Profiles in a Round Duct for Various Reynolds Numbers and Duct Roughness

Figure 4D - Changing Velocity Profiles

8

2.0

 AMCA 200-95 (R2011)

0.10 0.09 0.08 0.05

0.07

0.04 0.06

0.03

0.05

0.02 0.015

FULLY ROUGH (EQ 18) Eq. (29a)

0.04

0.010 0.008

           f

 ,      R       O      T       C 0.03      A      F      N       O      I      T       C      I      R      F

0.006

R    O   U    G   H    W    I    T    H    E    q  .  R    e   D    (    2    9  a   E    P     )   E    N    D   E    N    C   E   

0.02

0.004

0.002

0.0010 0.0008 0.0006

Eq. (27)

0.0004

SMOOTH PIPE Eqs. (28a) and (28b)

0.015

0.0002 LAMINAR

TRANSITION REGION

TURBULENT

0.00010 0.00005

0.010 0.009 0.008 103

2

3

5

104

2

3

5

105

2

3

5

106

2

3

5

107

2

3

5

0.00001 108

REYNOLDS NUMBER, Re

Figure 4E - Moody Diagram Reprinted by permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, Georgia, from the 1993  ASHRAE Handbook-Fundamentals. (Moody 1944). Values on the chart are the same for both the SI and I-P systems. Equation numbers refer  to equations in the source document.

9